Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_black 1 2.342328
beta3_pH 1 2.180852
beta3_black 1 1.682552
beta0_pH 2 1.631929
beta0_black 1 1.484581
beta3_yellow 2 1.311319
beta2_yellow 5 1.293227
beta2_black 1 1.275691
parameter n badRhat_avg
beta2_pH 13 1.257640
beta0_yellow 1 1.250384
beta1_pH 12 1.213756
beta1_yellow 5 1.168740
tau_beta0_yellow 2 1.154983
beta0_pelagic 1 1.148981
beta2_pelagic 2 1.148544
beta1_pelagic 3 1.132988
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta0_pelagic 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
beta0_pH 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
beta0_yellow 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
beta1_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta1_pelagic 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0
beta1_pH 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1
beta1_yellow 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0
beta2_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta2_pelagic 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0
beta2_pH 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1
beta2_yellow 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1
beta3_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
beta3_yellow 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.121 0.075 -0.249 -0.125 0.046
mu_bc_H[2] -0.091 0.047 -0.173 -0.096 0.015
mu_bc_H[3] -0.433 0.071 -0.561 -0.435 -0.285
mu_bc_H[4] -0.988 0.190 -1.385 -0.985 -0.622
mu_bc_H[5] 0.928 0.941 -0.174 0.747 3.259
mu_bc_H[6] -2.125 0.317 -2.762 -2.119 -1.507
mu_bc_H[7] -0.447 0.109 -0.662 -0.442 -0.239
mu_bc_H[8] 0.250 0.358 -0.348 0.221 1.044
mu_bc_H[9] -0.279 0.134 -0.555 -0.278 -0.005
mu_bc_H[10] -0.108 0.069 -0.234 -0.112 0.033
mu_bc_H[11] -0.125 0.038 -0.198 -0.124 -0.050
mu_bc_H[12] -0.254 0.107 -0.492 -0.249 -0.054
mu_bc_H[13] -0.135 0.079 -0.278 -0.137 0.023
mu_bc_H[14] -0.306 0.096 -0.508 -0.304 -0.126
mu_bc_H[15] -0.344 0.050 -0.441 -0.345 -0.243
mu_bc_H[16] -0.262 0.375 -0.897 -0.288 0.585
mu_bc_R[1] 1.340 0.146 1.047 1.341 1.628
mu_bc_R[2] 1.445 0.094 1.251 1.447 1.627
mu_bc_R[3] 1.405 0.141 1.135 1.407 1.672
mu_bc_R[4] 0.896 0.204 0.470 0.905 1.260
mu_bc_R[5] 1.163 0.447 0.258 1.175 2.015
mu_bc_R[6] -1.629 0.403 -2.417 -1.625 -0.879
mu_bc_R[7] 0.268 0.187 -0.107 0.272 0.638
mu_bc_R[8] 0.523 0.195 0.134 0.522 0.902
mu_bc_R[9] 0.300 0.214 -0.138 0.312 0.676
mu_bc_R[10] 1.320 0.156 1.002 1.325 1.611
mu_bc_R[11] 1.039 0.099 0.839 1.041 1.235
mu_bc_R[12] 0.821 0.207 0.396 0.822 1.222
mu_bc_R[13] 1.017 0.106 0.808 1.018 1.218
mu_bc_R[14] 0.900 0.138 0.626 0.901 1.174
mu_bc_R[15] 0.780 0.108 0.563 0.778 0.994
mu_bc_R[16] 1.090 0.125 0.834 1.090 1.335
tau_pH[1] 5.167 0.452 4.334 5.159 6.087
tau_pH[2] 2.029 0.225 1.629 2.021 2.498
tau_pH[3] 2.261 0.226 1.842 2.253 2.733
beta0_pH[1,1] 0.565 0.169 0.223 0.568 0.885
beta0_pH[2,1] 1.369 0.170 1.019 1.376 1.698
beta0_pH[3,1] 1.415 0.181 1.017 1.425 1.736
beta0_pH[4,1] 1.585 0.207 1.155 1.597 1.966
beta0_pH[5,1] -0.911 0.354 -1.709 -0.865 -0.379
beta0_pH[6,1] -0.844 0.519 -2.331 -0.749 -0.137
beta0_pH[7,1] -0.296 0.761 -1.503 -0.506 0.927
beta0_pH[8,1] -0.774 0.297 -1.518 -0.742 -0.297
beta0_pH[9,1] -0.751 0.351 -1.482 -0.717 -0.204
beta0_pH[10,1] 0.478 0.169 0.141 0.478 0.805
beta0_pH[11,1] -0.082 0.165 -0.421 -0.075 0.222
beta0_pH[12,1] 0.487 0.187 0.120 0.487 0.835
beta0_pH[13,1] 0.020 0.143 -0.256 0.022 0.294
beta0_pH[14,1] -0.317 0.171 -0.653 -0.318 0.011
beta0_pH[15,1] -0.028 0.182 -0.395 -0.024 0.326
beta0_pH[16,1] -0.508 0.375 -1.396 -0.451 0.053
beta0_pH[1,2] 2.793 0.180 2.429 2.797 3.140
beta0_pH[2,2] 2.893 0.148 2.602 2.893 3.192
beta0_pH[3,2] 3.124 0.276 2.237 3.174 3.471
beta0_pH[4,2] 2.963 0.147 2.657 2.964 3.233
beta0_pH[5,2] 5.018 1.709 2.931 4.627 9.392
beta0_pH[6,2] 3.121 0.213 2.708 3.122 3.534
beta0_pH[7,2] 1.958 0.172 1.619 1.958 2.299
beta0_pH[8,2] 2.863 0.176 2.537 2.864 3.203
beta0_pH[9,2] 3.434 0.224 3.017 3.432 3.873
beta0_pH[10,2] 3.622 0.218 3.195 3.621 4.045
beta0_pH[11,2] -4.833 0.302 -5.413 -4.836 -4.225
beta0_pH[12,2] -4.790 0.398 -5.587 -4.788 -4.011
beta0_pH[13,2] -4.583 0.402 -5.385 -4.601 -3.760
beta0_pH[14,2] -5.567 0.480 -6.575 -5.534 -4.711
beta0_pH[15,2] -4.294 0.346 -4.953 -4.300 -3.598
beta0_pH[16,2] -4.853 0.377 -5.633 -4.844 -4.123
beta0_pH[1,3] 0.712 0.527 -0.596 0.827 1.434
beta0_pH[2,3] 2.099 0.258 1.443 2.139 2.470
beta0_pH[3,3] 2.408 0.274 1.631 2.462 2.770
beta0_pH[4,3] 2.866 0.312 1.975 2.917 3.245
beta0_pH[5,3] 1.711 1.960 -1.033 1.351 6.639
beta0_pH[6,3] -0.307 0.997 -2.072 -0.478 1.588
beta0_pH[7,3] -1.998 0.542 -3.162 -1.956 -1.076
beta0_pH[8,3] 0.295 0.193 -0.079 0.297 0.673
beta0_pH[9,3] -0.639 0.486 -2.029 -0.554 0.010
beta0_pH[10,3] 0.133 1.012 -2.231 0.487 1.394
beta0_pH[11,3] -0.141 0.327 -0.755 -0.156 0.512
beta0_pH[12,3] -0.905 0.374 -1.701 -0.884 -0.271
beta0_pH[13,3] 0.025 0.417 -0.670 -0.023 0.904
beta0_pH[14,3] -0.261 0.264 -0.773 -0.264 0.249
beta0_pH[15,3] -0.693 0.301 -1.312 -0.682 -0.128
beta0_pH[16,3] -0.372 0.284 -0.934 -0.372 0.178
beta1_pH[1,1] 2.994 0.310 2.430 2.974 3.639
beta1_pH[2,1] 2.139 0.248 1.699 2.125 2.663
beta1_pH[3,1] 1.990 0.286 1.511 1.975 2.633
beta1_pH[4,1] 2.349 0.311 1.839 2.320 3.042
beta1_pH[5,1] 2.414 0.553 1.728 2.313 3.659
beta1_pH[6,1] 4.278 1.190 2.525 4.088 7.044
beta1_pH[7,1] 2.979 1.993 0.374 2.825 7.073
beta1_pH[8,1] 4.407 1.061 2.856 4.247 6.873
beta1_pH[9,1] 2.503 0.564 1.752 2.409 3.942
beta1_pH[10,1] 2.047 0.228 1.620 2.044 2.517
beta1_pH[11,1] 3.259 0.211 2.875 3.249 3.718
beta1_pH[12,1] 2.545 0.217 2.129 2.547 2.981
beta1_pH[13,1] 2.957 0.211 2.563 2.952 3.380
beta1_pH[14,1] 3.418 0.223 2.987 3.411 3.845
beta1_pH[15,1] 2.528 0.229 2.085 2.522 2.988
beta1_pH[16,1] 4.168 0.627 3.217 4.078 5.637
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.003 0.040 0.000 0.000 0.010
beta1_pH[3,2] 0.108 0.364 0.000 0.000 1.410
beta1_pH[4,2] 0.019 0.240 0.000 0.000 0.040
beta1_pH[5,2] 0.000 0.004 0.000 0.000 0.003
beta1_pH[6,2] 0.015 0.131 0.000 0.000 0.053
beta1_pH[7,2] 0.014 0.310 0.000 0.000 0.007
beta1_pH[8,2] 0.004 0.040 0.000 0.000 0.011
beta1_pH[9,2] 0.003 0.052 0.000 0.000 0.005
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.667 0.330 5.999 6.674 7.290
beta1_pH[12,2] 6.461 0.466 5.569 6.442 7.445
beta1_pH[13,2] 6.979 0.442 6.102 6.982 7.863
beta1_pH[14,2] 7.207 0.501 6.294 7.176 8.281
beta1_pH[15,2] 6.777 0.374 6.031 6.778 7.538
beta1_pH[16,2] 7.448 0.420 6.635 7.446 8.301
beta1_pH[1,3] 2.670 1.108 1.328 2.387 5.631
beta1_pH[2,3] 0.297 1.582 0.000 0.013 1.726
beta1_pH[3,3] 0.177 0.382 0.000 0.008 1.275
beta1_pH[4,3] 0.943 10.037 0.000 0.008 2.186
beta1_pH[5,3] 3.101 2.284 0.092 2.759 8.110
beta1_pH[6,3] 2.177 1.197 0.024 2.225 3.831
beta1_pH[7,3] 2.838 0.546 1.921 2.802 3.991
beta1_pH[8,3] 2.734 0.341 2.062 2.728 3.394
beta1_pH[9,3] 2.678 0.482 1.938 2.627 3.873
beta1_pH[10,3] 3.284 1.132 1.736 2.950 5.870
beta1_pH[11,3] 2.737 0.386 1.963 2.736 3.513
beta1_pH[12,3] 4.172 0.465 3.314 4.150 5.183
beta1_pH[13,3] 1.558 0.441 0.618 1.595 2.337
beta1_pH[14,3] 2.513 0.334 1.858 2.512 3.148
beta1_pH[15,3] 1.975 0.324 1.352 1.968 2.629
beta1_pH[16,3] 1.774 0.320 1.142 1.773 2.404
beta2_pH[1,1] 0.499 0.141 0.308 0.479 0.801
beta2_pH[2,1] 0.562 0.216 0.276 0.524 1.063
beta2_pH[3,1] 0.601 0.272 0.243 0.549 1.279
beta2_pH[4,1] 0.491 0.176 0.229 0.467 0.886
beta2_pH[5,1] 1.275 1.130 0.150 0.995 4.150
beta2_pH[6,1] 0.160 0.055 0.079 0.152 0.294
beta2_pH[7,1] -0.396 1.282 -4.076 0.017 0.787
beta2_pH[8,1] 0.210 0.070 0.113 0.197 0.372
beta2_pH[9,1] 0.388 0.229 0.125 0.352 0.807
beta2_pH[10,1] 0.612 0.189 0.345 0.583 1.048
beta2_pH[11,1] 0.782 0.216 0.470 0.746 1.285
beta2_pH[12,1] 1.360 0.509 0.755 1.249 2.637
beta2_pH[13,1] 0.743 0.229 0.411 0.705 1.312
beta2_pH[14,1] 0.830 0.211 0.515 0.800 1.336
beta2_pH[15,1] 0.813 0.312 0.407 0.761 1.597
beta2_pH[16,1] 0.363 0.167 0.176 0.315 0.819
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] -0.851 10.423 -21.173 -1.282 19.588
beta2_pH[3,2] -0.842 10.358 -21.452 -1.254 19.803
beta2_pH[4,2] -0.967 10.267 -20.936 -1.316 19.653
beta2_pH[5,2] 0.716 9.350 -19.179 1.022 18.687
beta2_pH[6,2] 0.710 9.355 -19.192 0.888 18.681
beta2_pH[7,2] 0.788 9.160 -18.916 0.768 18.640
beta2_pH[8,2] 0.742 9.367 -19.153 0.909 18.878
beta2_pH[9,2] 0.708 9.420 -19.593 1.074 18.502
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.657 4.272 -20.851 -8.655 -4.248
beta2_pH[12,2] -7.608 5.007 -19.936 -6.810 -0.887
beta2_pH[13,2] -7.381 4.900 -19.131 -6.241 -1.584
beta2_pH[14,2] -8.378 4.641 -19.816 -7.410 -2.438
beta2_pH[15,2] -9.442 4.323 -20.332 -8.520 -3.646
beta2_pH[16,2] -9.817 4.396 -21.516 -8.864 -3.950
beta2_pH[1,3] 2.729 3.668 0.138 0.757 12.167
beta2_pH[2,3] 2.795 4.375 -4.833 1.815 13.290
beta2_pH[3,3] 2.508 4.320 -5.049 1.904 11.686
beta2_pH[4,3] 2.781 4.247 -3.955 1.713 12.989
beta2_pH[5,3] 10.170 6.337 0.628 9.345 24.831
beta2_pH[6,3] 10.140 6.269 0.459 9.271 24.764
beta2_pH[7,3] 10.018 6.326 0.971 9.107 24.801
beta2_pH[8,3] 10.971 5.790 2.510 9.895 24.716
beta2_pH[9,3] 9.842 6.330 0.430 9.169 23.975
beta2_pH[10,3] 3.101 3.689 0.289 1.272 12.674
beta2_pH[11,3] -2.728 4.070 -18.817 -1.595 -0.616
beta2_pH[12,3] -2.750 3.589 -15.381 -1.770 -0.882
beta2_pH[13,3] -2.181 4.223 -16.171 -1.624 2.523
beta2_pH[14,3] -3.289 3.723 -16.087 -2.124 -0.892
beta2_pH[15,3] -3.441 3.710 -16.410 -2.258 -0.971
beta2_pH[16,3] -3.559 3.871 -17.012 -2.263 -0.887
beta3_pH[1,1] 35.767 0.815 34.185 35.755 37.404
beta3_pH[2,1] 33.477 1.097 31.497 33.415 35.886
beta3_pH[3,1] 33.644 1.019 31.730 33.648 35.745
beta3_pH[4,1] 33.803 1.199 31.633 33.748 36.323
beta3_pH[5,1] 28.043 1.562 26.401 27.600 32.363
beta3_pH[6,1] 38.932 3.370 32.526 38.846 45.305
beta3_pH[7,1] 28.045 8.317 18.362 25.722 44.924
beta3_pH[8,1] 40.363 2.358 36.082 40.190 45.335
beta3_pH[9,1] 30.640 1.842 27.843 30.451 34.560
beta3_pH[10,1] 33.120 0.952 31.343 33.078 35.049
beta3_pH[11,1] 30.325 0.464 29.435 30.325 31.237
beta3_pH[12,1] 30.162 0.398 29.353 30.175 30.910
beta3_pH[13,1] 33.208 0.585 32.108 33.183 34.423
beta3_pH[14,1] 32.040 0.462 31.187 32.018 33.019
beta3_pH[15,1] 31.182 0.634 29.960 31.172 32.417
beta3_pH[16,1] 32.056 1.050 30.247 31.927 34.385
beta3_pH[1,2] 30.059 7.984 18.455 29.215 44.838
beta3_pH[2,2] 29.733 7.909 18.436 28.713 44.850
beta3_pH[3,2] 30.951 8.304 18.509 30.183 44.622
beta3_pH[4,2] 29.931 8.092 18.341 28.966 44.818
beta3_pH[5,2] 29.936 7.861 18.541 28.873 44.822
beta3_pH[6,2] 29.920 7.883 18.533 29.192 44.811
beta3_pH[7,2] 30.013 7.907 18.436 29.222 44.687
beta3_pH[8,2] 30.024 7.931 18.510 29.259 44.659
beta3_pH[9,2] 30.148 8.015 18.511 29.146 45.060
beta3_pH[10,2] 29.833 7.884 18.399 28.887 44.860
beta3_pH[11,2] 43.407 0.176 43.120 43.391 43.780
beta3_pH[12,2] 43.183 0.196 42.852 43.143 43.682
beta3_pH[13,2] 43.861 0.146 43.488 43.900 44.040
beta3_pH[14,2] 43.296 0.197 43.051 43.246 43.796
beta3_pH[15,2] 43.412 0.194 43.108 43.387 43.808
beta3_pH[16,2] 43.491 0.189 43.161 43.485 43.839
beta3_pH[1,3] 38.991 2.155 34.314 39.535 43.356
beta3_pH[2,3] 30.992 7.965 18.447 31.099 44.972
beta3_pH[3,3] 31.046 8.370 18.443 30.643 44.919
beta3_pH[4,3] 29.600 7.889 18.454 28.488 44.729
beta3_pH[5,3] 27.397 6.876 18.380 25.882 42.883
beta3_pH[6,3] 27.767 6.621 18.682 25.776 44.420
beta3_pH[7,3] 26.576 0.924 25.084 26.430 28.806
beta3_pH[8,3] 41.495 0.238 41.073 41.490 41.923
beta3_pH[9,3] 33.119 1.585 26.584 33.535 34.220
beta3_pH[10,3] 35.147 1.468 31.707 35.728 36.946
beta3_pH[11,3] 41.722 0.798 40.123 41.740 43.144
beta3_pH[12,3] 41.751 0.388 40.987 41.767 42.506
beta3_pH[13,3] 40.210 5.076 29.430 42.516 44.605
beta3_pH[14,3] 41.086 0.563 39.900 41.105 42.142
beta3_pH[15,3] 42.622 0.680 41.086 42.725 43.717
beta3_pH[16,3] 42.904 0.726 41.316 43.008 44.076
beta0_pelagic[1] 2.210 0.130 1.953 2.210 2.461
beta0_pelagic[2] 1.518 0.120 1.287 1.520 1.753
beta0_pelagic[3] 0.081 0.429 -0.984 0.176 0.646
beta0_pelagic[4] 0.090 0.575 -1.515 0.234 0.836
beta0_pelagic[5] 1.168 0.251 0.659 1.173 1.646
beta0_pelagic[6] 1.465 0.276 0.868 1.485 1.964
beta0_pelagic[7] 1.635 0.215 1.233 1.620 2.124
beta0_pelagic[8] 1.759 0.202 1.377 1.753 2.192
beta0_pelagic[9] 2.500 0.317 1.873 2.506 3.078
beta0_pelagic[10] 2.498 0.211 2.034 2.511 2.895
beta0_pelagic[11] -0.025 0.443 -1.032 0.004 0.662
beta0_pelagic[12] 1.683 0.140 1.407 1.683 1.958
beta0_pelagic[13] 0.307 0.194 -0.133 0.324 0.632
beta0_pelagic[14] -0.146 0.285 -0.764 -0.118 0.324
beta0_pelagic[15] -0.260 0.135 -0.528 -0.258 -0.003
beta0_pelagic[16] 0.172 0.361 -0.752 0.272 0.635
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.026 0.617 0.352 0.876 2.796
beta1_pelagic[4] 1.104 0.592 0.318 0.948 2.745
beta1_pelagic[5] -0.078 0.312 -0.689 -0.075 0.522
beta1_pelagic[6] -0.103 0.466 -0.888 -0.162 0.778
beta1_pelagic[7] -0.014 0.304 -0.607 -0.015 0.592
beta1_pelagic[8] -0.001 0.278 -0.538 -0.007 0.559
beta1_pelagic[9] 0.204 0.490 -0.745 0.306 0.975
beta1_pelagic[10] 0.066 0.276 -0.453 0.066 0.597
beta1_pelagic[11] 3.855 1.065 2.261 3.784 6.262
beta1_pelagic[12] 2.810 0.320 2.215 2.799 3.425
beta1_pelagic[13] 3.033 0.741 1.859 2.948 4.646
beta1_pelagic[14] 4.635 1.070 3.000 4.481 6.879
beta1_pelagic[15] 2.940 0.256 2.447 2.940 3.414
beta1_pelagic[16] 4.124 1.332 2.765 3.498 7.370
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 2.196 2.422 0.076 1.228 8.439
beta2_pelagic[4] 2.536 2.478 0.207 1.661 9.024
beta2_pelagic[5] -0.010 0.669 -1.452 -0.004 1.371
beta2_pelagic[6] -0.096 0.691 -1.450 -0.153 1.358
beta2_pelagic[7] 0.025 0.656 -1.326 0.003 1.407
beta2_pelagic[8] 0.007 0.633 -1.289 0.006 1.380
beta2_pelagic[9] 0.183 0.665 -1.248 0.243 1.474
beta2_pelagic[10] 0.015 0.616 -1.267 0.020 1.388
beta2_pelagic[11] 1.155 2.981 0.110 0.229 10.143
beta2_pelagic[12] 5.833 4.943 0.931 4.325 19.066
beta2_pelagic[13] 0.694 1.381 0.192 0.422 2.745
beta2_pelagic[14] 0.296 0.200 0.151 0.270 0.580
beta2_pelagic[15] 5.977 4.726 1.191 4.608 19.071
beta2_pelagic[16] 3.642 4.991 0.150 1.131 17.462
beta3_pelagic[1] 29.709 7.784 18.436 28.593 44.639
beta3_pelagic[2] 29.816 7.908 18.464 28.673 44.768
beta3_pelagic[3] 29.171 4.092 21.983 29.298 39.521
beta3_pelagic[4] 25.155 2.799 20.041 25.300 31.064
beta3_pelagic[5] 30.023 8.215 18.433 28.587 45.232
beta3_pelagic[6] 31.991 6.659 18.874 31.902 44.081
beta3_pelagic[7] 29.603 7.783 18.442 28.676 45.119
beta3_pelagic[8] 29.035 7.867 18.386 27.395 44.773
beta3_pelagic[9] 31.024 6.014 19.370 31.074 43.020
beta3_pelagic[10] 29.249 8.190 18.463 27.520 45.030
beta3_pelagic[11] 42.111 2.079 37.562 42.528 45.630
beta3_pelagic[12] 43.463 0.279 43.006 43.448 43.981
beta3_pelagic[13] 42.949 1.377 40.418 42.886 45.659
beta3_pelagic[14] 42.695 1.713 39.201 42.726 45.703
beta3_pelagic[15] 43.158 0.271 42.534 43.168 43.662
beta3_pelagic[16] 43.288 0.977 41.200 43.234 45.629
mu_beta0_pelagic[1] 0.887 0.897 -1.107 0.942 2.609
mu_beta0_pelagic[2] 1.811 0.382 1.022 1.820 2.562
mu_beta0_pelagic[3] 0.292 0.461 -0.661 0.292 1.217
tau_beta0_pelagic[1] 0.730 0.736 0.057 0.501 2.743
tau_beta0_pelagic[2] 2.741 2.873 0.243 2.009 9.738
tau_beta0_pelagic[3] 1.500 1.127 0.162 1.214 4.451
beta0_yellow[1] -0.530 0.196 -0.936 -0.515 -0.214
beta0_yellow[2] 0.468 0.209 -0.054 0.493 0.797
beta0_yellow[3] -0.311 0.197 -0.712 -0.306 0.033
beta0_yellow[4] 0.778 0.320 -0.128 0.842 1.187
beta0_yellow[5] -1.231 0.415 -2.059 -1.236 -0.416
beta0_yellow[6] 0.272 0.219 -0.169 0.272 0.690
beta0_yellow[7] 1.033 0.223 0.705 1.048 1.344
beta0_yellow[8] 0.701 0.667 -1.217 0.937 1.292
beta0_yellow[9] -0.162 0.302 -0.698 -0.153 0.370
beta0_yellow[10] 0.237 0.153 -0.071 0.240 0.527
beta0_yellow[11] -1.847 0.645 -2.873 -1.940 -0.123
beta0_yellow[12] -3.690 0.441 -4.618 -3.664 -2.875
beta0_yellow[13] -3.755 0.469 -4.779 -3.719 -2.953
beta0_yellow[14] -2.082 0.591 -3.062 -2.144 -0.455
beta0_yellow[15] -2.889 0.447 -3.826 -2.871 -2.090
beta0_yellow[16] -2.398 0.507 -3.325 -2.422 -1.383
beta1_yellow[1] 0.642 1.012 0.000 0.412 2.692
beta1_yellow[2] 1.199 0.549 0.623 1.076 2.873
beta1_yellow[3] 0.698 0.330 0.076 0.688 1.390
beta1_yellow[4] 1.562 0.919 0.653 1.262 4.189
beta1_yellow[5] 3.107 1.650 1.406 2.845 5.967
beta1_yellow[6] 2.283 0.353 1.588 2.278 3.000
beta1_yellow[7] 5.747 5.401 1.207 3.958 21.194
beta1_yellow[8] 2.861 3.799 0.034 1.981 12.385
beta1_yellow[9] 1.668 0.486 0.878 1.634 2.701
beta1_yellow[10] 2.444 0.475 1.599 2.418 3.467
beta1_yellow[11] 2.050 0.536 0.774 2.085 3.023
beta1_yellow[12] 2.491 0.457 1.644 2.464 3.444
beta1_yellow[13] 2.885 0.475 2.069 2.846 3.903
beta1_yellow[14] 2.197 0.587 0.990 2.219 3.221
beta1_yellow[15] 2.133 0.448 1.342 2.107 3.082
beta1_yellow[16] 2.154 0.504 1.098 2.177 3.088
beta2_yellow[1] -2.640 2.563 -8.427 -2.010 0.888
beta2_yellow[2] -2.402 2.373 -8.620 -1.585 -0.113
beta2_yellow[3] -2.605 2.486 -9.088 -1.863 -0.106
beta2_yellow[4] -2.069 2.392 -8.608 -1.143 -0.085
beta2_yellow[5] -4.244 2.790 -10.782 -3.752 -0.543
beta2_yellow[6] 3.475 2.188 0.930 2.874 9.165
beta2_yellow[7] -4.062 2.687 -10.757 -3.569 -0.798
beta2_yellow[8] -2.132 4.038 -10.148 -2.094 6.676
beta2_yellow[9] 3.568 2.356 0.210 3.186 9.036
beta2_yellow[10] -4.508 2.721 -11.123 -4.038 -0.863
beta2_yellow[11] -4.074 2.383 -10.441 -3.500 -1.055
beta2_yellow[12] -4.343 2.320 -10.188 -3.831 -1.406
beta2_yellow[13] -4.121 2.152 -9.710 -3.572 -1.571
beta2_yellow[14] -4.226 2.388 -10.085 -3.739 -0.498
beta2_yellow[15] -3.838 2.199 -9.615 -3.331 -1.074
beta2_yellow[16] -4.414 2.328 -10.136 -3.853 -1.483
beta3_yellow[1] 26.949 7.630 18.249 24.157 44.615
beta3_yellow[2] 28.894 2.347 21.992 28.908 33.032
beta3_yellow[3] 32.770 3.457 23.293 32.838 39.728
beta3_yellow[4] 28.940 3.886 20.358 28.138 35.978
beta3_yellow[5] 33.301 1.479 30.212 33.376 35.400
beta3_yellow[6] 39.677 0.554 38.695 39.639 40.910
beta3_yellow[7] 20.094 1.993 18.354 19.918 23.661
beta3_yellow[8] 24.707 5.310 18.242 23.800 40.672
beta3_yellow[9] 37.789 1.755 36.057 37.573 42.980
beta3_yellow[10] 29.323 0.559 27.981 29.401 30.089
beta3_yellow[11] 44.287 3.571 31.359 45.346 45.972
beta3_yellow[12] 43.333 0.386 42.604 43.316 44.099
beta3_yellow[13] 44.851 0.382 44.020 44.920 45.526
beta3_yellow[14] 43.882 2.470 33.863 44.229 45.834
beta3_yellow[15] 45.190 0.524 44.144 45.205 45.968
beta3_yellow[16] 44.527 1.039 43.388 44.565 45.831
mu_beta0_yellow[1] 0.104 0.557 -1.027 0.103 1.244
mu_beta0_yellow[2] 0.131 0.483 -0.855 0.138 1.077
mu_beta0_yellow[3] -2.422 0.666 -3.447 -2.519 -0.815
tau_beta0_yellow[1] 2.226 4.539 0.100 1.236 9.068
tau_beta0_yellow[2] 1.275 1.699 0.143 0.961 4.035
tau_beta0_yellow[3] 1.321 1.574 0.084 0.839 5.301
beta0_black[1] 0.036 0.197 -0.342 0.038 0.397
beta0_black[2] 1.914 0.128 1.660 1.915 2.158
beta0_black[3] 1.317 0.127 1.068 1.317 1.573
beta0_black[4] 2.428 0.129 2.181 2.425 2.682
beta0_black[5] 1.623 2.084 -3.046 1.716 5.812
beta0_black[6] 1.642 2.019 -2.842 1.675 5.951
beta0_black[7] 1.597 1.950 -2.929 1.644 5.475
beta0_black[8] 1.292 0.222 0.861 1.294 1.730
beta0_black[9] 2.433 0.251 1.944 2.430 2.932
beta0_black[10] 1.472 0.134 1.207 1.472 1.741
beta0_black[11] 3.487 0.147 3.198 3.486 3.769
beta0_black[12] 4.850 0.166 4.518 4.849 5.173
beta0_black[13] -0.121 0.244 -0.616 -0.102 0.333
beta0_black[14] 2.852 0.152 2.551 2.852 3.158
beta0_black[15] 1.289 0.153 0.989 1.288 1.602
beta0_black[16] 4.274 0.156 3.970 4.274 4.581
beta2_black[1] 2.153 3.329 -4.788 2.096 9.368
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.066 1.730 -6.992 -1.511 -0.359
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 36.783 7.746 19.182 41.145 43.955
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.237 0.796 37.507 39.315 40.579
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.268 0.194 -0.650 -0.268 0.107
beta4_black[2] 0.240 0.179 -0.108 0.243 0.597
beta4_black[3] -0.938 0.189 -1.320 -0.935 -0.583
beta4_black[4] 0.415 0.209 0.012 0.413 0.834
beta4_black[5] 0.318 2.562 -4.300 0.215 5.717
beta4_black[6] 0.244 2.401 -4.512 0.189 5.128
beta4_black[7] 0.221 2.330 -4.504 0.169 5.332
beta4_black[8] -0.701 0.372 -1.448 -0.692 0.024
beta4_black[9] 1.489 1.012 -0.089 1.372 3.728
beta4_black[10] 0.031 0.187 -0.344 0.033 0.390
beta4_black[11] -0.699 0.208 -1.114 -0.700 -0.297
beta4_black[12] 0.169 0.314 -0.442 0.168 0.807
beta4_black[13] -1.183 0.220 -1.632 -1.182 -0.761
beta4_black[14] -0.183 0.227 -0.633 -0.187 0.282
beta4_black[15] -0.885 0.212 -1.312 -0.883 -0.467
beta4_black[16] -0.602 0.219 -1.026 -0.600 -0.174
mu_beta0_black[1] 1.309 0.881 -0.727 1.349 3.005
mu_beta0_black[2] 1.609 0.915 -0.457 1.658 3.344
mu_beta0_black[3] 2.536 0.994 0.411 2.576 4.431
tau_beta0_black[1] 0.714 0.694 0.060 0.500 2.601
tau_beta0_black[2] 1.921 3.490 0.053 0.843 10.895
tau_beta0_black[3] 0.234 0.159 0.048 0.196 0.638
beta0_dsr[11] -2.893 0.287 -3.467 -2.890 -2.332
beta0_dsr[12] 4.531 0.297 3.998 4.530 5.078
beta0_dsr[13] -1.364 0.325 -2.023 -1.347 -0.800
beta0_dsr[14] -3.678 0.502 -4.665 -3.672 -2.696
beta0_dsr[15] -1.934 0.279 -2.476 -1.942 -1.383
beta0_dsr[16] -3.004 0.366 -3.708 -3.002 -2.287
beta1_dsr[11] 4.832 0.303 4.255 4.833 5.434
beta1_dsr[12] 7.256 19.056 2.264 5.057 20.811
beta1_dsr[13] 2.865 0.377 2.280 2.839 3.579
beta1_dsr[14] 6.347 0.527 5.315 6.361 7.356
beta1_dsr[15] 3.329 0.277 2.760 3.333 3.851
beta1_dsr[16] 5.825 0.381 5.094 5.821 6.568
beta2_dsr[11] -8.353 2.385 -13.929 -7.975 -4.779
beta2_dsr[12] -7.129 2.593 -12.759 -6.987 -2.342
beta2_dsr[13] -6.479 2.784 -12.273 -6.409 -1.139
beta2_dsr[14] -6.243 2.727 -12.286 -6.165 -1.794
beta2_dsr[15] -7.852 2.457 -13.407 -7.537 -3.926
beta2_dsr[16] -8.016 2.352 -13.359 -7.703 -4.397
beta3_dsr[11] 43.488 0.150 43.212 43.481 43.783
beta3_dsr[12] 33.971 0.764 32.193 34.129 34.808
beta3_dsr[13] 43.247 0.324 42.826 43.185 43.861
beta3_dsr[14] 43.342 0.229 43.081 43.269 43.920
beta3_dsr[15] 43.511 0.187 43.174 43.507 43.861
beta3_dsr[16] 43.442 0.158 43.173 43.433 43.756
beta4_dsr[11] 0.584 0.207 0.182 0.579 0.999
beta4_dsr[12] 0.248 0.438 -0.603 0.247 1.160
beta4_dsr[13] -0.157 0.216 -0.581 -0.158 0.275
beta4_dsr[14] 0.145 0.248 -0.335 0.151 0.619
beta4_dsr[15] 0.726 0.212 0.306 0.724 1.144
beta4_dsr[16] 0.148 0.225 -0.302 0.153 0.597
beta0_slope[11] -1.936 0.163 -2.258 -1.936 -1.623
beta0_slope[12] -4.674 0.266 -5.223 -4.665 -4.165
beta0_slope[13] -1.393 0.265 -2.086 -1.363 -1.007
beta0_slope[14] -2.643 0.185 -3.007 -2.648 -2.275
beta0_slope[15] -1.372 0.169 -1.701 -1.369 -1.045
beta0_slope[16] -2.723 0.172 -3.062 -2.723 -2.396
beta1_slope[11] 4.594 0.283 4.049 4.592 5.168
beta1_slope[12] 5.023 0.518 4.039 5.006 6.037
beta1_slope[13] 3.057 0.722 2.275 2.895 5.418
beta1_slope[14] 6.526 0.548 5.512 6.520 7.640
beta1_slope[15] 3.054 0.283 2.513 3.052 3.620
beta1_slope[16] 5.370 0.397 4.625 5.357 6.149
beta2_slope[11] 8.035 2.347 4.454 7.658 13.407
beta2_slope[12] 7.117 2.540 2.509 6.908 12.682
beta2_slope[13] 5.403 3.123 0.275 5.619 11.404
beta2_slope[14] 6.519 2.468 2.376 6.313 12.041
beta2_slope[15] 7.620 2.464 3.631 7.308 13.338
beta2_slope[16] 7.638 2.312 4.055 7.367 13.187
beta3_slope[11] 43.476 0.153 43.204 43.471 43.779
beta3_slope[12] 43.411 0.230 43.058 43.379 43.864
beta3_slope[13] 43.654 0.536 42.861 43.712 44.967
beta3_slope[14] 43.325 0.174 43.093 43.289 43.770
beta3_slope[15] 43.516 0.197 43.155 43.517 43.876
beta3_slope[16] 43.460 0.170 43.172 43.455 43.806
beta4_slope[11] -0.576 0.218 -1.008 -0.575 -0.163
beta4_slope[12] -1.405 0.652 -2.902 -1.335 -0.361
beta4_slope[13] 0.065 0.222 -0.361 0.062 0.514
beta4_slope[14] -0.173 0.257 -0.665 -0.176 0.353
beta4_slope[15] -0.723 0.217 -1.142 -0.724 -0.306
beta4_slope[16] -0.200 0.238 -0.641 -0.200 0.262
sigma_H[1] 0.204 0.055 0.106 0.200 0.324
sigma_H[2] 0.170 0.030 0.119 0.169 0.235
sigma_H[3] 0.194 0.043 0.117 0.192 0.286
sigma_H[4] 0.418 0.075 0.297 0.408 0.588
sigma_H[5] 0.999 0.207 0.615 0.987 1.442
sigma_H[6] 0.415 0.199 0.049 0.412 0.823
sigma_H[7] 0.304 0.061 0.208 0.296 0.447
sigma_H[8] 0.407 0.086 0.259 0.398 0.594
sigma_H[9] 0.525 0.128 0.329 0.505 0.828
sigma_H[10] 0.209 0.043 0.135 0.206 0.300
sigma_H[11] 0.279 0.047 0.200 0.274 0.386
sigma_H[12] 0.434 0.166 0.207 0.403 0.781
sigma_H[13] 0.215 0.038 0.149 0.212 0.301
sigma_H[14] 0.506 0.092 0.342 0.500 0.704
sigma_H[15] 0.245 0.039 0.176 0.242 0.333
sigma_H[16] 0.225 0.043 0.153 0.221 0.318
lambda_H[1] 3.031 3.816 0.156 1.802 12.471
lambda_H[2] 7.914 7.582 0.787 5.792 28.938
lambda_H[3] 6.292 9.527 0.275 3.087 34.332
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 4.205 9.486 0.036 1.086 29.277
lambda_H[6] 7.295 13.083 0.009 1.247 43.732
lambda_H[7] 0.013 0.009 0.002 0.011 0.037
lambda_H[8] 8.430 10.701 0.202 4.849 38.534
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.288 0.463 0.033 0.191 1.010
lambda_H[11] 0.266 0.389 0.011 0.123 1.288
lambda_H[12] 4.667 6.213 0.194 2.585 20.453
lambda_H[13] 3.396 3.065 0.244 2.517 11.657
lambda_H[14] 3.348 3.994 0.215 2.093 15.240
lambda_H[15] 0.025 0.035 0.004 0.016 0.098
lambda_H[16] 0.807 1.098 0.047 0.428 3.655
mu_lambda_H[1] 4.288 1.887 1.200 4.158 8.482
mu_lambda_H[2] 3.907 1.929 0.771 3.762 8.089
mu_lambda_H[3] 3.511 1.842 0.776 3.224 7.618
sigma_lambda_H[1] 8.580 4.342 1.954 7.982 18.461
sigma_lambda_H[2] 8.523 4.628 1.346 7.932 18.482
sigma_lambda_H[3] 6.341 4.031 1.040 5.395 16.426
beta_H[1,1] 6.892 1.099 4.191 7.072 8.487
beta_H[2,1] 9.856 0.489 8.786 9.878 10.750
beta_H[3,1] 8.002 0.774 6.193 8.109 9.262
beta_H[4,1] 9.151 7.687 -7.068 9.433 23.301
beta_H[5,1] 0.117 2.251 -4.791 0.303 3.948
beta_H[6,1] 3.072 3.928 -7.149 4.580 7.508
beta_H[7,1] 0.466 5.868 -11.850 0.885 11.205
beta_H[8,1] 1.186 2.773 -2.051 1.196 3.265
beta_H[9,1] 12.751 5.849 1.255 12.610 24.330
beta_H[10,1] 7.049 1.703 3.584 7.115 10.368
beta_H[11,1] 5.139 3.545 -2.779 5.821 9.990
beta_H[12,1] 2.628 1.052 0.774 2.526 4.995
beta_H[13,1] 9.061 0.894 7.097 9.120 10.502
beta_H[14,1] 2.183 1.026 0.150 2.206 4.256
beta_H[15,1] -6.158 3.758 -12.902 -6.398 1.909
beta_H[16,1] 3.450 2.603 -0.746 3.154 9.552
beta_H[1,2] 7.899 0.253 7.396 7.906 8.375
beta_H[2,2] 10.016 0.138 9.741 10.020 10.287
beta_H[3,2] 8.959 0.202 8.559 8.955 9.379
beta_H[4,2] 3.618 1.479 0.824 3.551 6.607
beta_H[5,2] 1.969 0.963 0.005 1.982 3.812
beta_H[6,2] 5.732 0.999 3.446 5.882 7.336
beta_H[7,2] 2.654 1.134 0.647 2.584 5.032
beta_H[8,2] 3.034 0.894 1.560 3.129 4.182
beta_H[9,2] 3.510 1.132 1.308 3.484 5.758
beta_H[10,2] 8.190 0.344 7.494 8.192 8.864
beta_H[11,2] 9.775 0.640 8.852 9.653 11.247
beta_H[12,2] 3.938 0.358 3.263 3.943 4.658
beta_H[13,2] 9.128 0.250 8.671 9.115 9.657
beta_H[14,2] 4.022 0.355 3.346 4.010 4.708
beta_H[15,2] 11.369 0.686 9.984 11.415 12.615
beta_H[16,2] 4.525 0.808 3.016 4.512 6.132
beta_H[1,3] 8.451 0.243 8.013 8.435 8.965
beta_H[2,3] 10.066 0.119 9.836 10.066 10.296
beta_H[3,3] 9.616 0.163 9.296 9.612 9.955
beta_H[4,3] -2.567 0.873 -4.262 -2.575 -0.910
beta_H[5,3] 3.811 0.604 2.495 3.824 4.933
beta_H[6,3] 7.863 1.165 6.340 7.491 10.484
beta_H[7,3] -2.783 0.720 -4.210 -2.800 -1.369
beta_H[8,3] 5.200 0.425 4.631 5.157 5.996
beta_H[9,3] -2.913 0.742 -4.373 -2.913 -1.498
beta_H[10,3] 8.708 0.280 8.146 8.708 9.253
beta_H[11,3] 8.543 0.291 7.906 8.562 9.048
beta_H[12,3] 5.249 0.321 4.499 5.289 5.766
beta_H[13,3] 8.834 0.177 8.476 8.840 9.173
beta_H[14,3] 5.721 0.277 5.113 5.737 6.217
beta_H[15,3] 10.367 0.318 9.772 10.363 10.992
beta_H[16,3] 6.243 0.608 4.951 6.297 7.260
beta_H[1,4] 8.249 0.183 7.850 8.262 8.567
beta_H[2,4] 10.119 0.123 9.855 10.129 10.332
beta_H[3,4] 10.114 0.164 9.757 10.128 10.405
beta_H[4,4] 11.823 0.449 10.941 11.829 12.708
beta_H[5,4] 5.472 0.753 4.275 5.364 7.210
beta_H[6,4] 7.032 0.910 4.975 7.307 8.279
beta_H[7,4] 8.218 0.354 7.514 8.225 8.900
beta_H[8,4] 6.711 0.226 6.304 6.717 7.105
beta_H[9,4] 7.208 0.464 6.300 7.209 8.102
beta_H[10,4] 7.728 0.230 7.269 7.728 8.201
beta_H[11,4] 9.390 0.201 9.008 9.390 9.788
beta_H[12,4] 7.146 0.215 6.746 7.141 7.600
beta_H[13,4] 9.044 0.140 8.772 9.046 9.312
beta_H[14,4] 7.741 0.220 7.328 7.735 8.200
beta_H[15,4] 9.475 0.239 9.003 9.476 9.930
beta_H[16,4] 9.352 0.243 8.920 9.338 9.859
beta_H[1,5] 8.977 0.145 8.674 8.981 9.246
beta_H[2,5] 10.781 0.096 10.602 10.780 10.979
beta_H[3,5] 10.923 0.175 10.618 10.913 11.288
beta_H[4,5] 8.375 0.462 7.473 8.375 9.308
beta_H[5,5] 5.436 0.570 4.155 5.490 6.448
beta_H[6,5] 8.784 0.626 7.898 8.625 10.263
beta_H[7,5] 6.785 0.341 6.140 6.779 7.478
beta_H[8,5] 8.206 0.197 7.859 8.197 8.582
beta_H[9,5] 8.189 0.471 7.230 8.195 9.103
beta_H[10,5] 10.104 0.226 9.649 10.103 10.556
beta_H[11,5] 11.508 0.230 11.054 11.509 11.964
beta_H[12,5] 8.483 0.199 8.081 8.484 8.895
beta_H[13,5] 10.012 0.133 9.747 10.010 10.267
beta_H[14,5] 9.200 0.234 8.773 9.191 9.691
beta_H[15,5] 11.158 0.245 10.682 11.162 11.644
beta_H[16,5] 9.919 0.183 9.547 9.923 10.267
beta_H[1,6] 10.187 0.191 9.849 10.175 10.604
beta_H[2,6] 11.515 0.107 11.312 11.513 11.738
beta_H[3,6] 10.811 0.161 10.461 10.820 11.101
beta_H[4,6] 12.894 0.815 11.257 12.913 14.443
beta_H[5,6] 5.910 0.610 4.756 5.888 7.102
beta_H[6,6] 8.819 0.646 7.041 8.930 9.799
beta_H[7,6] 9.811 0.574 8.705 9.801 10.921
beta_H[8,6] 9.529 0.260 9.049 9.542 9.985
beta_H[9,6] 8.480 0.786 6.986 8.470 10.126
beta_H[10,6] 9.522 0.319 8.833 9.549 10.065
beta_H[11,6] 10.821 0.347 10.077 10.839 11.450
beta_H[12,6] 9.368 0.256 8.884 9.357 9.902
beta_H[13,6] 11.048 0.168 10.758 11.033 11.392
beta_H[14,6] 9.835 0.292 9.249 9.839 10.392
beta_H[15,6] 10.853 0.428 10.010 10.852 11.696
beta_H[16,6] 10.541 0.239 10.047 10.546 11.013
beta_H[1,7] 10.902 0.891 8.727 11.004 12.330
beta_H[2,7] 12.205 0.443 11.325 12.214 13.051
beta_H[3,7] 10.531 0.683 8.966 10.594 11.647
beta_H[4,7] 2.506 4.172 -5.341 2.501 10.484
beta_H[5,7] 6.403 1.812 2.952 6.398 10.281
beta_H[6,7] 9.604 2.336 4.821 9.590 15.454
beta_H[7,7] 10.646 2.844 5.183 10.660 16.320
beta_H[8,7] 10.951 0.964 9.500 10.922 12.414
beta_H[9,7] 4.365 4.041 -3.855 4.396 12.000
beta_H[10,7] 9.857 1.460 7.186 9.765 13.091
beta_H[11,7] 10.969 1.692 7.826 10.914 14.667
beta_H[12,7] 9.972 0.925 7.922 10.046 11.559
beta_H[13,7] 11.647 0.793 9.747 11.754 12.855
beta_H[14,7] 10.415 0.924 8.433 10.459 12.096
beta_H[15,7] 11.931 2.214 7.664 11.935 16.275
beta_H[16,7] 12.279 1.233 10.244 12.128 15.078
beta0_H[1] 9.027 12.849 -18.015 8.867 33.874
beta0_H[2] 10.494 6.483 -2.630 10.584 22.582
beta0_H[3] 9.651 9.849 -11.445 9.746 29.803
beta0_H[4] 4.867 188.235 -386.208 7.797 360.045
beta0_H[5] 4.224 24.772 -43.800 4.191 53.436
beta0_H[6] 8.144 46.255 -98.241 7.881 113.207
beta0_H[7] 2.321 132.979 -268.865 4.336 256.515
beta0_H[8] 7.376 27.227 -13.792 6.571 26.306
beta0_H[9] 3.935 125.933 -239.986 4.840 252.845
beta0_H[10] 8.452 32.971 -58.484 8.523 76.922
beta0_H[11] 10.293 48.288 -83.835 8.618 115.311
beta0_H[12] 6.579 11.232 -16.744 6.690 30.195
beta0_H[13] 10.069 10.747 -9.946 9.912 31.422
beta0_H[14] 7.172 11.604 -16.513 6.864 30.904
beta0_H[15] 11.372 106.698 -212.671 9.733 230.802
beta0_H[16] 8.098 25.731 -41.843 7.778 60.494